Fereydoon_Shekofte

Mr. Fereydoon Shekofte

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9 years, 314 days

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These are questions asked by Fereydoon_Shekofte

the principle is so easy as the method for demonstration of area of a disk by dissecting it to tiny sectors ...

and i just reversed the topic and i formed a shape by rearranging the tiny triangles that made the area of point and straight line as you can see in graph or interactively download the maple 18 worksheet that i attached ...

 

BUT my problem is that i can't yet underastand what is the formula or equation of this curve ?

the only obvious prperties of the curve is its ARC LENGTH that must be the half of straight line !
SO I NEED THE HELP OF PROFESSIONALs ?

also the programming and impelmenting of this subject in maple language was so hard for me !!!

I hope mapleprimes employee or developers offer more efficent and intelgent algorithm for using Maple in such cases ...

unknown_curve_by_shekofte.mw
 

ALGORITHM

hlf := proc (x, y, z, i) options operator, arrow; geometry[point](ds1, [x[1], x[2]]), geometry[point](ds2, [y[1], y[2]]), geometry[point](ds3, [z[1], z[2]]), geometry[dsegment](tt1, [ds2, ds3]), geometry[translation](dss, ds3, tt1), geometry[PerpenBisector](pb, ds3, ds1), geometry[reflection](ds4, dss, pb), assign(('crv[i, 1]', 'crv[i, 2]') = (geometry[HorizontalCoord](ds4), geometry[VerticalCoord](ds4))) end proc

proc (x, y, z, i) options operator, arrow; geometry[point](ds1, [x[1], x[2]]), geometry[point](ds2, [y[1], y[2]]), geometry[point](ds3, [z[1], z[2]]), geometry[dsegment](tt1, [ds2, ds3]), geometry[translation](dss, ds3, tt1), geometry[PerpenBisector](pb, ds3, ds1), geometry[reflection](ds4, dss, pb), assign(('crv[i, 1]', 'crv[i, 2]') = (geometry[HorizontalCoord](ds4), geometry[VerticalCoord](ds4))) end proc

(1)

MATRIX WITH DESIRE SIZE AND THREE INITIAL VALUES

crv := Matrix(400, 2, {(2, 1) = HFloat(1.0), (2, 2) = HFloat(0.0), (3, 1) = HFloat(1.0), (3, 2) = HFloat(0.1)}, datatype = float[8], storage = rectangular, order = Fortran_order, shape = [])

crv := Matrix(400, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = 1.0, (2, 2) = .0, (3, 1) = 1.0, (3, 2) = .1, (4, 1) = -0.1980198019801982e-1, (4, 2) = 0.9801980198019805e-1, (5, 1) = 1.0194211728865195, (5, 2) = .19809596344249814, (6, 1) = -0.57585751517988726e-1, (6, 2) = .19060698589266134, (7, 1) = 1.0559137411806545, (7, 2) = .2911996285652951, (8, 1) = -.1101731426397452, (8, 2) = .2756632396016475, (9, 1) = 1.1062163692195215, (9, 2) = .37762674012401487, (10, 1) = -.17416214658765472, (10, 2) = .3525098880240373, (11, 1) = 1.1671423424235312, (11, 2) = .4569238131415244, (12, 1) = -.2466255700808896, (12, 2) = .4214232557812443, (13, 1) = 1.2360557101807381, (13, 2) = .5293872366347594, (14, 1) = -.3253094338429394, (14, 2) = .48313913366915184, (15, 1) = 1.3109487458308529, (15, 2) = .595652108256989, (16, 1) = -.408567746414083, (16, 2) = .5385291452940439, (17, 1) = 1.3903473987423378, (17, 2) = .656445643405403, (18, 1) = -.495222799209344, (18, 2) = .5884380806167939, (19, 1) = 1.4731818019427334, (19, 2) = .7124676180799383, (20, 1) = -.5844340423821378, (20, 2) = .6336194273382524, (21, 1) = 1.558673790835259, (21, 2) = .7643436225058795, (22, 1) = -.6755973629522178, (22, 2) = .6747199015768401, (23, 1) = 1.6462521625681776, (23, 2) = .8126139944187906, (24, 1) = -.768273483034192, (24, 2) = .7122850019567344, (25, 1) = 1.7354923582507662, (25, 2) = .8577381284773329, (26, 1) = -.8621385794010603, (26, 2) = .7467718644414333, (27, 1) = 1.8260744290544424, (27, 2) = .9001042523136931, (28, 1) = -.9569505091805229, (28, 2) = .7785633408383272, (29, 1) = 1.9177538611154679, (29, 2) = .9400402227785242, (30, 1) = -1.0525256440627835, (30, 2) = .8079809136858231, (31, 1) = 2.0103412288236853, (31, 2) = .97782354371334, (32, 1) = -1.1487228445027227, (32, 2) = .8352957196986452, (33, 1) = 2.103687872783331, (33, 2) = 1.0136900191670435, (34, 1) = -1.2454322462280305, (34, 2) = .860737646078795, (35, 1) = 2.197675702033759, (35, 2) = 1.0478409774668087, (36, 1) = -1.3425673140215706, (36, 2) = .8845027171862903, (37, 1) = 2.2922098421158257, (37, 2) = 1.0804492027933132, (38, 1) = -1.4400591369052527, (38, 2) = .906759052707141, (39, 1) = 2.387213267433803, (39, 2) = 1.1116637695506997, (40, 1) = -1.5378522792667093, (40, 2) = .9276516664036538, (41, 1) = 2.4826228333296245, (41, 2) = 1.1416139738166264, (42, 1) = -1.635901725574782, (42, 2) = .9473063370618, (43, 1) = 2.578386307440582, (43, 2) = 1.1704125332632354, (44, 1) = -1.734170603348866, (44, 2) = .9658327414895891, (45, 1) = 2.6744601230711718, (45, 2) = 1.198158198693699, (46, 1) = -1.8326284667701598, (46, 2) = .9833270014200253, (47, 1) = 2.770807660389581, (47, 2) = 1.2249378934768282, (48, 1) = -1.9312499889549857, (48, 2) = .9998737643042781, (49, 1) = 2.867397917870683, (49, 2) = 1.2508284739982083, (50, 1) = -2.030013955484974, (50, 2) = 1.0155479122958924, (51, 1) = 2.9642044754014845, (51, 2) = 1.2758981851859215, (52, 1) = -2.1289024824111373, (52, 2) = 1.0304159734463314, (53, 1) = 3.061204677621959, (53, 2) = 1.3002078698648063, (54, 1) = -2.227900403227824, (54, 2) = 1.0445372932845332, (55, 1) = 3.158378985196276, (55, 2) = 1.3238119785633315, (56, 1) = -2.3269947842657284, (56, 2) = 1.0579650126260454, (57, 1) = 3.2557104553194773, (57, 2) = 1.3467594168442423, (58, 1) = -2.4261745385759257, (58, 2) = 1.0707468878784756, (59, 1) = 3.3531843225532487, (59, 2) = 1.3690942597246591, (60, 1) = -2.525430116002866, (60, 2) = 1.0829259826578275, (61, 1) = 3.450787658195739, (61, 2) = 1.390856356853824, (62, 1) = -2.624753252674097, (62, 2) = 1.0945412537174226, (63, 1) = 3.548509091606773, (63, 2) = 1.4120818474745995, (64, 1) = -2.7241367671830483, (64, 2) = 1.1056280496409003, (65, 1) = 3.64633858077174, (65, 2) = 1.43280360053078, (66, 1) = -2.823574393732581, (66, 2) = 1.1162185371743174, (67, 1) = 3.7442672222719096, (67, 2) = 1.4530515923801233, (68, 1) = -2.923060644736592, (68, 2) = 1.1263420672486881, (69, 1) = 3.8422870930015427, (69, 2) = 1.4728532322653893, (70, 1) = -3.0225906970527, (70, 2) = 1.136025490504571, (71, 1) = 3.9403911176217967, (71, 2) = 1.4922336438530825, (72, 1) = -3.1221602972884583, (72, 2) = 1.145293430345279, (73, 1) = 4.038572957003524, (73, 2) = 1.5112159096720095, (74, 1) = -3.2217656825924834, (74, 2) = 1.1541685201158893, (75, 1) = 4.1368269138837945, (75, 2) = 1.5298212840936567, (76, 1) = -3.3214035140867813, (76, 2) = 1.1626716098551355, (77, 1) = 4.235147852715831, (77, 2) = 1.548069379533639, (78, 1) = -3.421070820673153, (78, 2) = 1.1708219471376027, (79, 1) = 4.333531131281794, (79, 2) = 1.5659783297712109, (80, 1) = -3.520764951395804, (80, 2) = 1.1786373357686766, (81, 1) = 4.431972542101462, (81, 2) = 1.5835649336455564, (82, 1) = -3.620483534894472, (82, 2) = 1.186134275478924, (83, 1) = 4.530468262036541, (83, 2) = 1.600844781864521, (84, 1) = -3.720224444760148, (84, 2) = 1.1933280852600467, (85, 1) = 4.629014808782039, (85, 2) = 1.617832369231097, (86, 1) = -3.8199857698257804, (86, 2) = 1.2002330125695062, (87, 1) = 4.7276090031694675, (87, 2) = 1.6345411942374746, (88, 1) = -3.919765788600015, (88, 2) = 1.206862330288027, (89, 1) = 4.826247936394211, (89, 2) = 1.6509838476816228, (90, 1) = -4.0195629471928465, (90, 2) = 1.213228423029804, (91, 1) = 4.924928941431071, (91, 2) = 1.6671720917159443, (92, 1) = -4.119375840195512, (92, 2) = 1.2193428641684605, (93, 1) = 5.0236495680250846, (93, 2) = 1.6831169305324716, (94, 1) = -4.219203194068761, (94, 2) = 1.2252164847439373, (95, 1) = 5.122407560745161, (95, 2) = 1.698828673717137, (96, 1) = -4.3190438526683055, (96, 2) = 1.230859435249552, (97, 1) = 5.221200839670427, (97, 2) = 1.714316993160968, (98, 1) = -4.418896764597212, (98, 2) = 1.2362812411587893, (99, 1) = 5.320027483346861, (99, 2) = 1.7295909742939517, (100, 1) = -4.518760972125019, (100, 2) = 1.2414908529334576, (101, 1) = 5.418885713707807, (101, 2) = 1.7446591623038485, (102, 1) = -4.6186356014544945, (102, 2) = 1.2464966911549156, (103, 1) = 5.517773882698374, (103, 2) = 1.7595296039143944, (104, 1) = -4.7185198541510305, (104, 2) = 1.251306687335172, (105, 1) = 5.616690460382383, (105, 2) = 1.7742098852224268, (106, 1) = -4.818412999577848, (106, 2) = 1.2559283208922685, (107, 1) = 5.715634024342858, (107, 2) = 1.7887071660294933, (108, 1) = -4.918314368203739, (108, 2) = 1.2603686527124744, (109, 1) = 5.814603250214132, (109, 2) = 1.8030282110486413, (110, 1) = -5.018223345669672, (110, 2) = 1.2646343556687651, (111, 1) = 5.913596903206451, (111, 2) = 1.8171794183199657, (112, 1) = -5.118139367517097, (112, 2) = 1.2687317424194353, (113, 1) = 6.012613830503219, (113, 2) = 1.831166845127858, (114, 1) = -5.21806191449458, (114, 2) = 1.2726667907713844, (115, 1) = 6.111652954427307, (115, 2) = 1.8449962316778337, (116, 1) = -5.317990508371122, (116, 2) = 1.2764451668586307, (117, 1) = 6.2107132662867155, (117, 2) = 1.8586730227604047, (118, 1) = -5.41792470819436, (118, 2) = 1.2800722463571568, (119, 1) = 6.309793820821663, (119, 2) = 1.8722023876030995, (120, 1) = -5.517864106940267, (120, 2) = 1.2835531339316275, (121, 1) = 6.408893731185266, (121, 2) = 1.885589238088756, (122, 1) = -5.617808328508073, (122, 2) = 1.2868926810872656, (123, 1) = 6.508012164398588, (123, 2) = 1.898838245498212, (124, 1) = -5.717757025020236, (124, 2) = 1.290095502580743, (125, 1) = 6.607148337228266, (125, 2) = 1.9119538559180023, (126, 1) = -5.817709874392481, (126, 2) = 1.293165991526965, (127, 1) = 6.706301512441308, (127, 2) = 1.9249403044383377, (128, 1) = -5.917666578143407, (128, 2) = 1.2961083333237493, (129, 1) = 6.8054709953971475, (129, 2) = 1.9378016282532036, (130, 1) = -6.0176268594169855, (130, 2) = 1.2989265185033287, (131, 1) = 6.904656130941838, (131, 2) = 1.9505416787625545, (132, 1) = -6.117590461194588, (132, 2) = 1.3016243546081112, (133, 1) = 7.003856300573377, (133, 2) = 1.9631641327661697, (134, 1) = -6.21755714467603, (134, 2) = 1.3042054771780078, (135, 1) = 7.103070919850769, (135, 2) = 1.9756725028295183, (136, 1) = -6.317526687811594, (136, 2) = 1.306673359927663, (137, 1) = 7.202299436022552, (137, 2) = 1.9880701468938442, (138, 1) = -6.417498883969152, (138, 2) = 1.3090313241840286, (139, 1) = 7.301541325853255, (139, 2) = 2.0003602771954387, (140, 1) = -6.5174735407223325, (140, 2) = 1.3112825476476813, (141, 1) = 7.400796093628638, (141, 2) = 2.012545968552697, (142, 1) = -6.617450478747347, (142, 2) = 1.313430072535057, (143, 1) = 7.50006326932267, (143, 2) = 2.024630166073826, (144, 1) = -6.717429530817475, (144, 2) = 1.3154768131532322, (145, 1) = 7.5993424069110365, (145, 2) = 2.0366156923330117, (146, 1) = -6.817410540885456, (146, 2) = 1.3174255629539324, (147, 1) = 7.698633082817586, (147, 2) = 2.0485052540583215, (148, 1) = -6.917393363245122, (148, 2) = 1.3192790011090527, (149, 1) = 7.797934894481557, (149, 2) = 2.0603014483705757, (150, 1) = -7.0173778617645555, (150, 2) = 1.321039698646012, (151, 1) = 7.8972474590346895, (151, 2) = 2.0720067686087926, (152, 1) = -7.117363909183894, (152, 2) = 1.3227101241777621, (153, 1) = 7.996570412078425, (153, 2) = 2.0836236097745826, (154, 1) = -7.217351386471633, (154, 2) = 1.3242926492590916, (155, 1) = 8.095903406552413, (155, 2) = 2.095154273624947, (156, 1) = -7.31734018223395, (156, 2) = 1.3257895533980282, (157, 1) = 8.19524611168639, (157, 2) = 2.106600973440315, (158, 1) = -7.417330192172108, (158, 2) = 1.3272030287486039, (159, 1) = 8.294598212028305, (159, 2) = 2.1179658384923075, (160, 1) = -7.517321318583555, (160, 2) = 1.3285351845089273, (161, 1) = 8.393959406542223, (161, 2) = 2.1292509182335895, (162, 1) = -7.61731346990274, (162, 2) = 1.3297880510464566, (163, 1) = 8.493329407770212, (163, 2) = 2.140458186230258, (164, 1) = -7.7173065602780975, (164, 2) = 1.330963583770492, (165, 1) = 8.592707941052902, (165, 2) = 2.151589543855484, (166, 1) = -7.817300509181985, (166, 2) = 1.3320636667702082, (167, 1) = 8.692094743803963, (167, 2) = 2.1626468237615546, (168, 1) = -7.917295241050697, (168, 2) = 1.3330901162350286, (169, 1) = 8.79148956483414, (169, 2) = 2.17363179314606, (170, 1) = -8.017290684951938, (170, 2) = 1.3340446836727593, (171, 1) = 8.890892163720926, (171, 2) = 2.1845461568266593, (172, 1) = -8.117286774277405, (172, 2) = 1.3349290589396254, (173, 1) = 8.990302310220263, (173, 2) = 2.1953915601377187, (174, 1) = -8.217283446458348, (174, 2) = 1.3357448730952464, (175, 1) = 9.089719783717038, (175, 2) = 2.2061695916610335, (176, 1) = -8.317280642702178, (176, 2) = 1.3364937010945086, (177, 1) = 9.189144372711352, (177, 2) = 2.2168817858018923, (178, 1) = -8.417278307748376, (178, 2) = 1.3371770643273901, (179, 1) = 9.288575874337885, (179, 2) = 2.2275296252208676, (180, 1) = -8.51727638964211, (180, 2) = 1.3377964330169019, (181, 1) = 9.38801409391586, (181, 2) = 2.238114543130887, (182, 1) = -8.617274839524129, (182, 2) = 1.3383532284845332, (183, 1) = 9.487458844527328, (183, 2) = 2.248637925468447, (184, 1) = -8.717273611435608, (184, 2) = 1.338848825291885, (185, 1) = 9.586909946621702, (185, 2) = 2.259101112947129, (186, 1) = -8.81727266213676, (186, 2) = 1.3392845532665083, (187, 1) = 9.686367227644634, (187, 2) = 2.2695054030009856, (188, 1) = -8.917271950938124, (188, 2) = 1.3396616994193669, (189, 1) = 9.785830521689496, (189, 2) = 2.279852051624801, (190, 1) = -9.01727143954354, (190, 2) = 1.3399815097608, (191, 1) = 9.885299669169834, (191, 2) = 2.290142275117709, (192, 1) = -9.117271091903897, (192, 2) = 1.3402451910213613, (193, 1) = 9.984774516511353, (193, 2) = 2.3003772517361876, (194, 1) = -9.21727087408083, (194, 2) = 1.3404539122834236, (195, 1) = 10.084254915862049, (195, 2) = 2.3105581232620165, (196, 1) = -9.317270754119619, (196, 2) = 1.340608806529065, (197, 1) = 10.183740724819254, (197, 2) = 2.3206859964903903, (198, 1) = -9.417270701930574, (198, 2) = 1.3407109721093091, (199, 1) = 10.283231806172436, (199, 2) = 2.330761944643004, (200, 1) = -9.517270689178297, (200, 2) = 1.3407614741394762, (201, 1) = 10.382728027660692, (201, 2) = 2.340787008710608, (202, 1) = -9.617270689178213, (202, 2) = 1.3407613458250416, (203, 1) = 10.482229261743957, (203, 2) = 2.3507621987291967, (204, 1) = -9.717270676799862, (204, 2) = 1.3407115897221153, (205, 1) = 10.581735385387018, (205, 2) = 2.360688494993737, (206, 1) = -9.817270628376434, (206, 2) = 1.340613178936369, (207, 1) = 10.6812462798555, (207, 2) = 2.3705668492130583, (208, 1) = -9.917270521620122, (208, 2) = 1.3404670582639766, (209, 1) = 10.78076183052304, (209, 2) = 2.3803981856092897, (210, 1) = -10.017270335542845, (210, 2) = 1.340274145277895, (211, 1) = 10.880281926688948, (211, 2) = 2.3901834019650092, (212, 1) = -10.117270050382006, (212, 2) = 1.3400353313626012, (213, 1) = 10.979806461405664, (213, 2) = 2.39992337062105, (214, 1) = -10.217269647530875, (214, 2) = 1.3397514827001804, (215, 1) = 11.079335331315425, (215, 2) = 2.4096189394277356, (216, 1) = -10.31726910947333, (216, 2) = 1.339423441210489, (217, 1) = 11.17886843649554, (217, 2) = 2.4192709326521147, (218, 1) = -10.417268419722603, (218, 2) = 1.3390520254479306, (219, 1) = 11.278405680311755, (219, 2) = 2.4288801518436194, (220, 1) = -10.517267562763804, (220, 2) = 1.3386380314572164, (221, 1) = 11.377946969279217, (221, 2) = 2.4384473766604065, (222, 1) = -10.617266523999925, (222, 2) = 1.3381822335903517, (223, 1) = 11.477492212930567, (223, 2) = 2.4479733656585063, (224, 1) = -10.717265289701118, (224, 2) = 1.3376853852869233, (225, 1) = 11.577041323690738, (225, 2) = 2.4574588570457663, (226, 1) = -10.817263846957006, (226, 2) = 1.3371482198196523, (227, 1) = 11.676594216758058, (227, 2) = 2.466904569402453, (228, 1) = -10.91726218363185, (228, 2) = 1.3365714510070488, (229, 1) = 11.776150809991291, (229, 2) = 2.4763112023702676, (230, 1) = -11.01726028832235, (230, 2) = 1.3359557738948915, (231, 1) = 11.87571102380226, (231, 2) = 2.485679437311423, (232, 1) = -11.11725815031794, (232, 2) = 1.3353018654081579, (233, 1) = 11.975274781053738, (233, 2) = 2.495009937939321, (234, 1) = -11.217255759563406, (234, 2) = 1.334610384974921, (235, 1) = 12.074842006962298, (235, 2) = 2.5043033509222887, (236, 1) = -11.31725310662365, (236, 2) = 1.3338819751236488, (237, 1) = 12.174412629005845, (237, 2) = 2.513560306461744, (238, 1) = -11.417250182650509, (238, 2) = 1.3331172620552616, (239, 1) = 12.273986576835556, (239, 2) = 2.5227814188460744, (240, 1) = -11.51724697935146, (240, 2) = 1.3323168561911984, (241, 1) = 12.373563782191994, (241, 2) = 2.531967286981442, (242, 1) = -11.61724348896011, (242, 2) = 1.3314813526987077, (243, 1) = 12.473144178825155, (243, 2) = 2.5411184949006618, (244, 1) = -11.717239704208351, (244, 2) = 1.3306113319944717, (245, 1) = 12.57272770241824, (245, 2) = 2.550235612251222, (246, 1) = -11.817235618300094, (246, 2) = 1.329707360227638, (247, 1) = 12.672314290514938, (247, 2) = 2.559319194763473, (248, 1) = -11.91723122488645, (248, 2) = 1.328769989743256, (249, 1) = 12.77190388245004, (249, 2) = 2.5683697846999345, (250, 1) = -12.017226518042307, (250, 2) = 1.3277997595270632, (251, 1) = 12.8714964192832, (251, 2) = 2.577387911286639, (252, 1) = -12.117221492244191, (252, 2) = 1.326797195632515, (253, 1) = 12.971091843735675, (253, 2) = 2.5863740911273467, (254, 1) = -12.217216142349347, (254, 2) = 1.3257628115909013, (255, 1) = 13.07069010012989, (255, 2) = 2.5953288286014606, (256, 1) = -12.31721046357596, (256, 2) = 1.3246971088053434, (257, 1) = 13.170291134331679, (257, 2) = 2.6042526162463906, (258, 1) = -12.417204451484448, (258, 2) = 1.3236005769294308, (259, 1) = 13.269894893695065, (259, 2) = 2.6131459351250985, (260, 1) = -12.517198101959776, (260, 2) = 1.322473694231205, (261, 1) = 13.36950132700944, (261, 2) = 2.622009255179501, (262, 1) = -12.617191411194707, (262, 2) = 1.321316927943172, (263, 1) = 13.469110384449028, (263, 2) = 2.6308430355703867, (264, 1) = -12.717184375673952, (264, 2) = 1.32013073459897, (265, 1) = 13.568722017524523, (265, 2) = 2.639647725004448, (266, 1) = -12.817176992159169, (266, 2) = 1.3189155603573148, (267, 1) = 13.668336179036778, (267, 2) = 2.648423762049022, (268, 1) = -12.917169257674749, (268, 2) = 1.3176718413137758, (269, 1) = 13.767952823032449, (269, 2) = 2.6571715754350738, (270, 1) = -13.017161169494347, (270, 2) = 1.3164000038009407, (271, 1) = 13.867571904761498, (271, 2) = 2.6658915843489646, (272, 1) = -13.11715272512813, (272, 2) = 1.3151004646774762, (273, 1) = 13.967193380636468, (273, 2) = 2.674584198713481, (274, 1) = -13.217143922310681, (274, 2) = 1.313773631606583, (275, 1) = 14.06681720819343, (275, 2) = 2.683249819458609, (276, 1) = -13.317134758989527, (276, 2) = 1.3124199033242943, (277, 1) = 14.166443346054534, (277, 2) = 2.6918888387824906, (278, 1) = -13.41712523331427, (278, 2) = 1.3110396698980673, (279, 1) = 14.266071753892078, (279, 2) = 2.7005016404029916, (280, 1) = -13.517115343626271, (280, 2) = 1.309633312976095, (281, 1) = 14.365702392394034, (281, 2) = 2.709088599800275, (282, 1) = -13.61710508844886, (282, 2) = 1.3082012060277095, (283, 1) = 14.465335223230948, (283, 2) = 2.7176500844507765, (284, 1) = -13.717094466478049, (284, 2) = 1.3067437145752803, (285, 1) = 14.56497020902416, (285, 2) = 2.726186454052925, (286, 1) = -13.817083476573716, (286, 2) = 1.305261196417956, (287, 1) = 14.664607313315273, (287, 2) = 2.734698060744982, (288, 1) = -13.917072117751228, (288, 2) = 1.3037540018475924, (289, 1) = 14.764246500536817, (289, 2) = 2.743185249315299, (290, 1) = -14.017060389173494, (290, 2) = 1.3022224738571855, (291, 1) = 14.863887735984068, (291, 2) = 2.751648357405329, (292, 1) = -14.117048290143412, (292, 2) = 1.300666948342132, (293, 1) = 14.963530985787939, (293, 2) = 2.760087715705675, (294, 1) = -14.217035820096694, (294, 2) = 1.299087754294598, (295, 1) = 15.063176216888916, (295, 2) = 2.7685036481454657, (296, 1) = -14.317022978595046, (296, 2) = 1.2974852139912891, (297, 1) = 15.16282339701199, (297, 2) = 2.776896472075339, (298, 1) = -14.417009765319689, (298, 2) = 1.2958596431748846, (299, 1) = 15.262472494642534, (299, 2) = 2.785266498444272, (300, 1) = -14.516996180065195, (300, 2) = 1.2942113512293756, (301, 1) = 15.362123479003083, (301, 2) = 2.7936140319705083, (302, 1) = -14.616982222733638, (302, 2) = 1.2925406413495817, (303, 1) = 15.461776320030989, (303, 2) = 2.8019393713068355, (304, 1) = -14.716967893329013, (304, 2) = 1.290847810705046, (305, 1) = 15.561430988356891, (305, 2) = 2.810242809200408, (306, 1) = -14.816953191951946, (306, 2) = 1.2891331505985515, (307, 1) = 15.661087455283988, (307, 2) = 2.818524632647351, (308, 1) = -14.91693811879465, (308, 2) = 1.2873969466194581, (309, 1) = 15.760745692768063, (309, 2) = 2.8267851230423413, (310, 1) = -15.016922674136131, (310, 2) = 1.2856394787920657, (311, 1) = 15.860405673398233, (311, 2) = 2.8350245563233485, (312, 1) = -15.116906858337623, (312, 2) = 1.2838610217191921, (313, 1) = 15.960067370378395, (313, 2) = 2.8432432031117494, (314, 1) = -15.216890671838248, (314, 2) = 1.2820618447211607, (315, 1) = 16.05973075750933, (315, 2) = 2.851441328847962, (316, 1) = -15.316874115150878, (316, 2) = 1.2802422119703567, (317, 1) = 16.159395809171464, (317, 2) = 2.859619193922795, (318, 1) = -15.416857188858206, (318, 2) = 1.2784023826215303, (319, 1) = 16.2590625003082, (319, 2) = 2.867777053804653, (320, 1) = -15.516839893608992, (320, 2) = 1.2765426109380082, (321, 1) = 16.35873080640988, (321, 2) = 2.8759151591627723, (322, 1) = -15.616822230114503, (322, 2) = 1.2746631464139617, (323, 1) = 16.45840070349827, (323, 2) = 2.884033755986621, (324, 1) = -15.716804199145102, (324, 2) = 1.2727642338928775, (325, 1) = 16.5580721681116, (325, 2) = 2.8921330857016065, (326, 1) = -15.816785801527022, (326, 2) = 1.2708461136823792, (327, 1) = 16.65774517729012, (327, 2) = 2.9002133852812437, (328, 1) = -15.91676703813928, (328, 2) = 1.268909021665523, (329, 1) = 16.75741970856215, (329, 2) = 2.9082748873558875, (330, 1) = -16.01674790991074, (330, 2) = 1.2669531894087096, (331, 1) = 16.85709573993059, (331, 2) = 2.9163178203181714, (332, 1) = -16.116728417817317, (332, 2) = 1.2649788442663215, (333, 1) = 16.956773249859907, (333, 2) = 2.924342408425271, (334, 1) = -16.2167085628793, (334, 2) = 1.2629862094822095, (335, 1) = 17.05645221726355, (335, 2) = 2.932348871898094, (336, 1) = -16.316688346158827, (336, 2) = 1.2609755042881479, (337, 1) = 17.156132621491775, (337, 2) = 2.9403374270175253, (338, 1) = -16.416667768757446, (338, 2) = 1.2589469439993572, (339, 1) = 17.255814442319885, (339, 2) = 2.948308286217816, (340, 1) = -16.516646831813816, (340, 2) = 1.2569007401072017, (341, 1) = 17.35549765993686, (341, 2) = 2.9562616581772185, (342, 1) = -16.61662553650151, (342, 2) = 1.2548371003691625, (343, 1) = 17.455182254934353, (343, 2) = 2.964197747905985, (344, 1) = -16.716603884026913, (344, 2) = 1.2527562288961858, (345, 1) = 17.55486820829605, (345, 2) = 2.9721167568317868, (346, 1) = -16.816581875627225, (346, 2) = 1.2506583262374833, (347, 1) = 17.654555501387364, (347, 2) = 2.9800188828826726, (348, 1) = -16.916559512568554, (348, 2) = 1.2485435894628902, (349, 1) = 17.75424411594547, (349, 2) = 2.987904320567638, (350, 1) = -17.01653679614409, (350, 2) = 1.2464122122428551, (351, 1) = 17.85393403406965, (351, 2) = 2.99577326105489, (352, 1) = -17.116513727672398, (352, 2) = 1.244264384926145, (353, 1) = 17.953625238211966, (353, 2) = 3.003625892247887, (354, 1) = -17.216490308495736, (354, 2) = 1.2421002946153439, (355, 1) = 18.053317711168198, (355, 2) = 3.011462398859227, (356, 1) = -17.316466539978496, (356, 2) = 1.2399201252402174, (357, 1) = 18.153011436069086, (357, 2) = 3.019282962482459, (358, 1) = -17.416442423505703, (358, 2) = 1.2377240576290238, (359, 1) = 18.25270639637184, (359, 2) = 3.027087761661891, (360, 1) = -17.516417960481583, (360, 2) = 1.235512269577829, (361, 1) = 18.352402575851915, (361, 2) = 3.0348769719604447, (362, 1) = -17.61639315232819, (362, 2) = 1.233284935917888, (363, 1) = 18.452099958595046, (363, 2) = 3.0426507660256434, (364, 1) = -17.716368000484113, (364, 2) = 1.2310422285811824, (365, 1) = 18.55179852898951, (365, 2) = 3.0504093136537844, (366, 1) = -17.816342506403238, (366, 2) = 1.2287843166641488, (367, 1) = 18.651498271718648, (367, 2) = 3.0581527818523537, (368, 1) = -17.916316671553552, (368, 2) = 1.2265113664896643, (369, 1) = 18.751199171753584, (369, 2) = 3.0658813349007423, (370, 1) = -18.016290497416026, (370, 2) = 1.2242235416673544, (371, 1) = 18.850901214346198, (371, 2) = 3.073595134409324, (372, 1) = -18.11626398548354, (372, 2) = 1.2219210031522638, (373, 1) = 18.950604385022288, (373, 2) = 3.0812943393769356, (374, 1) = -18.216237137259842, (374, 2) = 1.219603909301958, (375, 1) = 19.05030866957493, (375, 2) = 3.088979106246827, (376, 1) = -18.316209954258593, (376, 2) = 1.217272415932095, (377, 1) = 19.15001405405806, (377, 2) = 3.096649588961116, (378, 1) = -18.416182438002412, (378, 2) = 1.2149266763705149, (379, 1) = 19.249720524780226, (379, 2) = 3.1043059390138033, (380, 1) = -18.516154590022012, (380, 2) = 1.2125668415099065, (381, 1) = 19.349428068298526, (381, 2) = 3.1119483055023873, (382, 1) = -18.616126411855333, (382, 2) = 1.2101930598590847, (383, 1) = 19.449136671412727, (383, 2) = 3.119576835178133, (384, 1) = -18.716097905046748, (384, 2) = 1.2078054775929261, (385, 1) = 19.54884632115956, (385, 2) = 3.1271916724950226, (386, 1) = -18.81606907114629, (386, 2) = 1.2054042386009987, (387, 1) = 19.648557004807166, (387, 2) = 3.134792959657441, (388, 1) = -18.916039911708925, (388, 2) = 1.202989484534943, (389, 1) = 19.748268709849718, (389, 2) = 3.142380836666629, (390, 1) = -19.01601042829384, (390, 2) = 1.2005613548546221, (391, 1) = 19.847981424002167, (391, 2) = 3.1499554413659463, (392, 1) = -19.11598062246379, (392, 2) = 1.1981199868730976, (393, 1) = 19.947695135195183, (393, 2) = 3.1575169094849778, (394, 1) = -19.21595049578447, (394, 2) = 1.195665515800449, (395, 1) = 20.047409831570192, (395, 2) = 3.1650653746825133, (396, 1) = -19.315920049823895, (396, 2) = 1.1931980747864839, (397, 1) = 20.147125501474594, (397, 2) = 3.1726009685884518, (398, 1) = -19.41588928615184, (398, 2) = 1.1907177949623766, (399, 1) = 20.24684213345708, (399, 2) = 3.1801238208446416, (400, 1) = -19.515858206339296, (400, 2) = 1.18822480548125}, datatype = float[8])

(2)

ATTENTION TO INITIAL VALUES

crv[1 .. 3]

Matrix([[0., 0.], [1., 0.], [1., .100000000000000]])

(3)

CYCLE EXCEPTIONS

hlf(crv[1], crv[2], crv[3], 4);

hlf(crv[3], crv[1], crv[4], 5)

ds1, ds2, ds3, tt1, dss, pb, ds4

 

ds1, ds2, ds3, tt1, dss, pb, ds4

(4)

GENERATED DATA SAMPLES

seq(hlf(crv[i-2], crv[i-3], crv[i-1], i), i = 6 .. 400):

MERGING SECTIONS

plots[display](seq(plots[polygonplot](crv[i .. i+2], scaling = constrained, color = [blue, green][irem(i, 2)+1], axes = none), i = 3 .. 10))

 

PLOT OF CURVES

plots[pointplot](crv[1 .. 300], axes = none, symbol = point, symbolsize = 20, color = red, scaling = constrained, connect = false)

 

plots[pointplot](crv[1 .. 10], axes = none, symbol = asterisk, symbolsize = 20, color = red, scaling = constrained, connect = false)

 

plots[display](seq(plots[polygonplot]([[0, 0], [1, (1/10)*i], [1, (i+1)*(1/10)]], scaling = constrained, color = [blue, green][irem(i, 2)+1], axes = none), i = 0 .. 10))

 

``

``


 

Download unknown_curve_by_shekofte.mw

 

this is a terrible maple crash just for a simple option !!!

only when i want to print the "x^2+y^2" in the caption of plot it raise exception !
but for some formulae there is no problem !
some technical guide or advise is needed ?
may someone check maple 2018 for this issue too ?

shekofte003.mw

salute ! all Maplesoft managers and employee programers ...

Is there any fortune in near future to have some kind of machin based "Proof Assistant" as built in part of Maple IDE ?

it can be better than COQ ?


also there is a great lack of user interactivity by Geometry and Geometry3d packages of maple !!!

for example most of the time it is nessesary (and more facilated) to define geometrical primitive shapes manually or making simple transformations and dissectings attaching ... rather than doing them programaticaly or by commands ?

even having traditional tools like compass ruler ... in pallettes of Geometry window ?


BEST WISHES FOR MAPLESOFT

 

I want to calculate the ratio of the length of day and night for every latitude on earth ?
but i confused on using Maple in a wise way for finding the formula !
this is my demonstration :

shekofte000.mw
 

Equations

 

the grat circle that divides the earth's surface into two dark and bright sides

[sin(t)*cos(tilt), cos(t), sin(t)*sin(tilt)]

[sin(t)*cos(tilt), cos(t), sin(t)*sin(tilt)]

(1.1)

circle of revolving of a point on earth in 24 hours

[sin(t)*cos(Latitude), cos(t)*cos(Latitude), sin(Latitude)]

[sin(t)*cos(Latitude), cos(t)*cos(Latitude), sin(Latitude)]

(1.2)

Visualization of dark and bright side the of earth

 

Explore(plots[display](plots[spacecurve]({[sin(t)*cos(tilt), cos(t), sin(t)*sin(tilt), color = red], [sin(t)*cos(Latitude), cos(t)*cos(Latitude), sin(Latitude), color = blue]}, t = 0 .. 2*Pi, scaling = constrained, thickness = 4, labels = [x, y, Latitudez], labeldirections = [horizontal, horizontal, vertical], axes = frame), plottools[rotate](plottools[hemisphere]([0, 0, 0], 1, capped = false, color = green, grid = [10, 10], style = surface), 0, tilt, 0), plottools[rotate](plottools[hemisphere]([0, 0, 0], 1, capped = false, color = black, grid = [10, 10], style = surface), 0, Pi+tilt, 0)), parameters = [tilt = 0 .. Pi, Latitude = -(1/2)*Pi .. (1/2)*Pi], initialvalues = [tilt = (1/2)*Pi+.409, Latitude = 1.16])

``


 

Download shekofte000.mw

 

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